ind a set of symmetric equations of aline that is parallel to the xz-plane that passes through the point(1,2,7). There are many lines that satisfy this condition, you just need to give me one such line. Hint: as a reminder, below are two examples of symmetric equations of a line:

Q: The plane through the points (-4,-8,-1), (8,3,5), (7,8,6) has equation Ax + By + Cz= D. If A = - 19…

A: Since plane passes through the given points therefore

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

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Q: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: The line whose equation is given as: (x-2z-2=0, y-22 -0) intersects the plane (x-2y+2-1-0) at the…

A: Given: x-2z-2=0 y-2z=0 equation of plane x-2y+z-1=0

Q: QUESTION 2 a) What is the equation of the straight line that passes through the points (1,-4) and…

A:

Q: 4- Find the line that passes through the point l2) the Point of intersection of the lines x+2y=3 and…

A: 4.  The equation of the line passing through a point x1,y1=1,2 and the point of intersection of the…

Q: 4) Find the equation of the line that is orthogonal to the line r = (1,-3+ 2t, 6- 2t) %3D and…

A: Given, x=1 y=-3+2t z=6-2t From the line equation, v=(0,2,-2) and P0=(3,0,3) Substitute the values,

Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: 5) Find the equation of the plane through the following point that also contains the given line. P =…

A: To find the equation of a plane through a point and parallel to a given line, we can use the…

Q: Answer the questions in detalied steps and show work. (7 and 8)

A: Step 1: Step 2:   Take x-axis and y-axis                 they intersect at (0,0) in two-space and…

Q: How many points are equidistant from two intersecting lines and 3 units from their point of…

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Q: Converting coordinates Express the following polar coordinates in Cartesian coordinates.

A: From the given data:

Q: If the lines a₁x + b₁y+C₁ = 0 and a₂x + b₂y + C₂ = 0 cut the coordinate axes at concyclic points,…

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Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: In each case, determine whether or not the lines have a single point of intersection. If they do,…

A: (a)

Q: 3) The straight line l passes through the points (0,1,5) and (2, –2, 1). Find the y - and z…

A: Using Cartesian equation.

Q: 1) Given the following equations of a certain line, determine the equation of the perpendicular line…

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Q: Question: please find the equation of the plane that contains the intersecting lines L1 (t) = + t…

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